One of the most successful method in quantifying the structures in the Cosmic Web is the Minkowski Functionals. In 3D, there are four minkowski Functionals: Area, Volume, Integrated Mean Curvature and the Integrated Gaussian Curvature. For defining the Minkowski Functionals one should define a surface. We have developed a method based on Marching cube 33 algorithm to generate a surface from a discrete data sets. Next we calculate the Minkowski Functionals and Shapefinder from the triangulated polyhedral surface. Applying this methodology to different data sets , we obtain interesting results related to geometry, morphology and topology of the large scale structure

One of the main goals in cosmology is to understand how the Universe evolves, how it forms structures, why it expands, and what is the nature of dark matter and dark energy. Next decade large and expensive observational projects will bring information on the structure and the distribution of many millions of galaxies at different redshifts enabling us to make great progress in answering these questions. However, these data require a very special and complex set of analysis tools to extract the maximum valuable information. Statistical inference techniques are being developed, bridging the gaps between theory, simulations, and observations. In particular, we discuss the efforts to address the question: What is the underlying nonlinear matter distribution and dynamics at any cosmic time corresponding to a set of observed galaxies in redshift space?

An accurate reconstruction of the initial conditions encodes the full phase-space information at any later cosmic time (given a particular structure formation model and a set of cosmological parameters). We present advances to solve this problem in a self-consistent way with Big Data techniques of the Cosmic Web.

Analysis of three-dimensional cosmological surveys has the potential to answer outstanding questions on the initial conditions from which structure appeared, and therefore on the very high energy physics at play in the early Universe. We report on recently proposed statistical data analysis methods designed to study the primordial large-scale structure via physical inference of the initial conditions in a fully Bayesian framework, and applications to the Sloan Digital Sky Survey data release 7. We illustrate how this approach led to a detailed characterization of the dynamic cosmic web underlying the observed galaxy distribution, based on the tidal environment.

We describe the Bayesian \barcode\ formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the basis of observational data, without the need for a correction of redshift space artifacts. In this contribution we provide a general overview of the the Cosmic Web connection with clusters and a description of the Bayesian BARCODE formalism. We conclude with a presentation of its successful workings with respect to test runs based on a simulated large scale matter distribution, in physical space as well as in redshift space.

We determine the auto-correlation function (ACF) of galaxies using massive deep galaxy surveys for which distances to individual objects are assessed using photometric redshifts. The method is applied to the 2deg COSMOS survey of ~ 300000 galaxies with i + < 25 and zph ≲ 3. The distance estimates based on photometric redshifts are not sufficiently accurate to be directly used to determine the ACF. Nevertheless, the photometric redshifts carry statistical information on the data distribution on (very) large scales. The investigation of the surface distribution of galaxies in several redshift (=distance) bins allows us to determine the spatial (3D) ACF over the redshift range of 0.2 - 3.2 or look back time of 2.4 - 11.5 Gy.

A quantitative study of the clustering properties of galaxies in the cosmic web as a function of absolute magnitude and colour is presented using the SDSS Data Release 7 galaxy redshift survey. We compare our results with mock galaxy samples obtained with four different semi-analytical models of galaxy formation imposed on the merger trees of the Millenium simulation.

Our recent estimates of galaxy counts and the luminosity density in the near-infrared (Keenan et al. 2010, 2012) indicated that the local universe may be under-dense on radial scales of several hundred megaparsecs. Such a large-scale local under-density could introduce significant biases in the measurement and interpretation of cosmological observables, such as the inferred effects of dark energy on the rate of expansion. In Keenan et al. (2013), we measured the K-band luminosity density as a function of distance from us to test for such a local under-density. We made this measurement over the redshift range 0.01 < z < 0.2 (radial distances D ~ 50 - 800 h70−1 Mpc). We found that the shape of the K-band luminosity function is relatively constant as a function of distance and environment. We derive a local (z < 0.07, D < 300 h70−1 Mpc) K-band luminosity density that agrees well with previously published studies. At z > 0.07, we measure an increasing luminosity density that by z ~ 0.1 rises to a value of ~ 1.5 times higher than that measured locally. This implies that the stellar mass density follows a similar trend. Assuming that the underlying dark matter distribution is traced by this luminous matter, this suggests that the local mass density may be lower than the global mass density of the universe at an amplitude and on a scale that is sufficient to introduce significant biases into the measurement of basic cosmological observables. At least one study has shown that an under-density of roughly this amplitude and scale could resolve the apparent tension between direct local measurements of the Hubble constant and those inferred by Planck team. Other theoretical studies have concluded that such an under-density could account for what looks like an accelerating expansion, even when no dark energy is present.

We have initiated the search and detailed study of large scale structures present in the universe using galaxy redshift surveys. In this process, we take the volume-limited sample of galaxies from Sloan Digital Sky Survey III and find very large structures even beyond the redshift of 0.2. One of the structures is even greater than 600 Mpc which raises a question on the homogeneity scale of the universe. The shapes of voids-structures (adjacent to each other) seem to be correlated, which supports the physical existence of the observed structures. The other observational supports include galaxy clusters' and QSO distribution's correlation with the density peaks of the volume limited sample of galaxies.

We derive constraints on radio source clustering towards Planck-selected galaxy clusters using the NVSS point source catalog. The constraint can be used for making a more realistic Sunyaev-Zeldovich effect (SZE) mocks, calculating predictions of detectable clusters count and for quantifying source confusion in radio surveys.

A compendium of over 8000 galaxy distances has been accumulated. Distance measurements permit the separation of observed velocities into cosmic expansion and peculiar velocity components. Only the radial component of peculiar velocities can be measured and individual errors are large, but a Wiener Filter procedure permits the reconstruction of three-dimensional motions and the density field that is responsible for these motions. A coherent flow pervades the entire domain of ± 15,000 km/s. Techniques are discussed for the separation of local and tidal components of the flow. Laniakea supercluster is identified as a region of contiguous infalling flows.

Comparison of galaxy flows with those predicted from the local galaxy distribution ended as an active field after two analyses came to vastly different conclusions 25 years ago, but that was due to faulty data. All the old results are therefore suspect. With new data collected in the last several years, the problem deserves another look. The goal is to explain the 640 km/s dipole anisotropy of the CMBR. For this we analyze the gravity field inferred from the enormous data set derived from the 2MASS collection of galaxies (Huchra et al. 2005), and compare it to the velocity field derived from the well calibrated SFI++ Tully-Fisher catalog (Springob et al. 2007). Using the “Inverse Method” to minimize Malmquist biases, within 10,000 km/s the gravity field is seen to predict the velocity field (Davis et al. 2011) to remarkable consistency. This is a beautiful demonstration of linear perturbation theory and is fully consistent with standard values of the cosmological variables.

Using redshifts from the 2M++ redshift compilation, we reconstruct the density of galaxies within 200 h−1 Mpc, and compare the predicted peculiar velocities Tully-Fisher and SNe peculiar velocities. The comparison yields a best-fit value of β ≡ Ωm0.55/b* = 0.431 ± 0.021, suggesting Ωm0.55σ8,lin = 0.401 ± 0.024, in good agreement with other probes. The predicted peculiar velocity of the Local Group from sources within the 2M++ volume is 540 ± 40 km s−1, towards l = 268° ± 4°, b = 38° ± 6°, which is misaligned by only 10° with the Cosmic Microwave Background dipole. To account for sources outside the 2M++ volume, we fit simultaneously for β* and an external bulk flow in our analysis. The external bulk flow has a velocity of 159 ± 23 km s−1 towards l = 304° ± 11°, b6° ± 13°.

We present results of analysis of the dark matter (DM) pairwise velocity statistics in different Cosmic Web environments. We use the DM velocity and density field from the Millennium 2 simulation together with the NEXUS+ algorithm to segment the simulation volume into voxels uniquely identifying one of the four possible environments: nodes, filaments, walls or cosmic voids. We show that the PDFs of the mean infall velocities v12 as well as its spatial dependence together with the perpendicular and parallel velocity dispersions bear a significant signal of the large-scale structure environment in which DM particle pairs are embedded. The pairwise flows are notably colder and have smaller mean magnitude in wall and voids, when compared to much denser environments of filaments and nodes. We discuss on our results, indicating that they are consistent with a simple theoretical predictions for pairwise motions as induced by gravitational instability mechanism. Our results indicate that the Cosmic Web elements are coherent dynamical entities rather than just temporal geometrical associations. In addition it should be possible to observationally test various Cosmic Web finding algorithms by segmenting available peculiar velocity data and studying resulting pairwise velocity statistics.

We describe preliminary measurements of the pairwise velocity dispersion (PVD) of galaxies in the Galaxy and Mass Assembly (GAMA) survey as a function of projected separation and galaxy luminosity. Due to the faint magnitude limit (r < 19.8) and highly-complete spectroscopic sampling of the GAMA survey, we are able to measure the PVD to smaller scales and for lower-luminosity galaxies than previous SDSS-based work. We see no strong scale-dependence at most luminosities in the quasi-linear regime. We observe an apparent drop in PVD towards very small scales (below ≈ 0.1h−1 Mpc), but this could in part be due to a restriction of the streaming model employed. At intermediate scales, the PVD is highest (~ 500 km/s) at intermediate luminosities, dropping at both fainter and brighter luminosities.

Peculiar motion introduces systematic variations in the observed luminosity distribution of galaxies. This allows one to constrain the cosmic peculiar velocity field from large galaxy redshift surveys. Using around half a million galaxies from the SDSS Data Release 7 at z ~ 0.1, we demonstrate the applicability of this approach to large datasets and obtain bounds on peculiar velocity moments and σ8, the amplitude of the linear matter power spectrum. Our results are in good agreement with the ΛCDM model and consistent with the previously reported ~ 1% zero-point tilt in the SDSS photometry. Finally, we discuss the prospects of constraining the growth rate of density perturbations by reconstructing the full linear velocity field from the observed galaxy clustering in redshift space.

While recent years have seen rapid growth in the number of galaxy peculiar velocity measurements, disagreements remain about the extent to which the peculiar velocity field - a tracer of the large-scale distribution of mass - agrees with both ΛCDM expectations and with velocity field models derived from redshift surveys. The 6dF Galaxy Survey includes peculiar velocities for nearly 9 000 early-type galaxies (6dFGSv), making it the largest and most homogeneous galaxy peculiar velocity sample to date. We have used the 6dFGS velocity field to determine the amplitude and scale of large-scale cosmic flows in the local universe and test standard cosmological models. We also compare the galaxy density and peculiar velocity fields to establish the distribution of dark and luminous matter and better constrain key cosmological parameters such as the redshift-space distortion parameter.

As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.

We investigate the accuracy achievable on measurements of the the growth rate of structure f(z) using redshift-space distortions (RSD), when (a) these are measured on the group-galaxy cross correlation function; (b) the latter is expanded over a modified version of the conventional spherical armonics, “truncated multipole moments”. Simulation results give first indications that this combination can push systematic errors on f(z) below 3%, using scales r ⩾ 10h−1 Mpc.

Quasars, as the most luminous persistent sources in the Universe, have broad applications for cosmological studies. In particular, they can be employed to directly measure the expansion history of the Universe, similarly to SNe Ia. The advantage of quasars is that they are numerous, cover a broad range of redshifts, up to z = 7, and do not show significant evolution of metallicity with redshift. The idea is based on the relation between the time delay of an emission line and the continuum, and the absolute monochromatic luminosity of a quasar. For intermediate redshift quasars, the suitable line is Mg II. Between December 2012 and March 2014, we performed five spectroscopic observations of the QSO CTS C30.10 (z = 0.900) using the South African Large Telesope (SALT), supplemented with photometric monitoring, with the aim of determining the variability of the line shape, changes in the total line intensity and in the continuum. We show that the method is very promising.

The accurate description of the properties of the Lyman-α forest is a spectacular success of the Cold Dark Matter theory of cosmological structure formation. After a brief review of early models, it is shown how numerical simulations have demonstrated the Lyman-α forest emerges from the cosmic web in the quasi-linear regime of overdensity. The quasi-linear nature of the structures allows accurate modeling, providing constraints on cosmological models over a unique range of scales and enabling the Lyman-α forest to serve as a bridge to the more complex problem of galaxy formation.